Field of the Invention
Embodiments of the present invention relate generally to computer simulations and, more specifically, to techniques for warm starting finite element analyses with deep neural networks.
Description of the Related Art
Finite element analysis (FEA) is a tool that can be used to simulate a variety of different physical processes. For example, FEA may be applied to simulate heat transfer through a structure. Typically, an FEA simulation includes a mesh of distinct nodes that are coupled together and a system of governing equations that describe how the distinct nodes interact with one another. In the above heat transfer example, the structure could be represented as a triangular mesh of distinct nodes, and heat transfer equations would describe how heat is exchanged between adjacent nodes within the triangular mesh.
A conventional FEA simulation typically executes an FEA solver to iteratively solve the governing equations of the simulation until a set of values is determined that does not “violate” those equations, within a reasonable error tolerance. The FEA solver is said to converge when an appropriate set of values is reached. One drawback to conventional FEA simulations, however, is that, with highly complex geometries, FEA solvers may take a long time to converge. Long wait times can be problematic because oftentimes many different designs need to be simulated before a particular design can be selected. In addition, FEA solvers often execute on shared computing resources that are both costly to use and time-restricted, which can add substantial cost and lead time to engineering projects.
As the foregoing illustrates, what is needed in the art is a more effective approach to increasing the convergence rates of FEA solvers.